to be published in Physics Letters B FERMILAB-Pub 95/199-T hep-lat/9507010Abstract We demonstrate that lattice QCD calculations can be made 10 3 -10 6 times faster by using very coarse lattices. To obtain accurate results, we replace the standard lattice actions by perturbativelyimproved actions with tadpole-improved correction terms that remove the leading errors due to the lattice. To illustrate the power of this approach, we calculate the static-quark potential, and the charmonium spectrum and wavefunctions using a desktop computer. We obtain accurate results that are independent of the lattice spacing and agree well with experiment.

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We discuss a program for replacing standard perturbative methods with Monte Carlo simulations in short distance lattice gauge theory calculations.In principle, perturbation theory is unnecessary to solve QCD with lattice methods. Even the short distance calculations relating the lattice action to continuum actions could in principle be done by a → 0, V → ∞ brute force Monte Carlo calculations. In practise, perturbation theory has been essential to the progress of lattice methods. It is much easier and more powerful than Monte Carlo for some purposes:• The a → 0, V → ∞ limits are much easier to take in perturbative calculations.• The values of perturbative coefficients can be calculated much more accurately than typical quantities in numerical calculations.

We study in detail the prediction for the semileptonic decaysB → D(D * )πℓν by heavy quark and chiral symmetry. The branching ratio forB → Dπℓν is quite significant, as big as (0.5 − 1)%. The branching ratio forB → D * πℓν is only of order 10 −4 − 10 −5 . Numerical results for various single particle spectra and their dependence on the pion momentum cutoff schemes are presented in a series of figures, as are the model independent ratios for differential rates of D and D * . We also study the parity-violation effects on the decay rates for different polarization states of the D * .